Mathematics & Statistics Colloquium: Alex Clark

Speaker: Alex Clark, University of Leicester (http://www2.le.ac.uk/departments/mathematics/extranet/staff-material/staff-profiles/adc20)

Title: Tiling Spaces:  Their Structure and Unexpected Examples

Abstract: In this talk we will explain how one can introduce a natural topological structure to certain spaces of tilings of the plane. These spaces admit a natural dynamical system that  captures many of the important properties of the tilings, including the spectral properties of associated quasicrystals. After a review of some of the fundamental results about the structure of these tiling spaces, we shall explain some recent results of Clark and Sadun that have far reaching implications for higher dimensional dynamical systems.
In particular, we shall explore a counterexample to conjectures which has the consequence that higher dimensional dynamics are fundamentally different from those of dimension one.

Faculty host: Krystyna Kuperberg